Monatshefte für Mathematik

, Volume 179, Issue 2, pp 191–199 | Cite as

Invariants of domains with finite GK dimension

  • Jeffrey BergenEmail author
  • Piotr Grzeszczuk


This paper examines the invariants of automorphisms, derivations, and \(q\)-skew derivations of finitely generated domains with finite GK dimension. We generalize results on centralizers obtained by Bell and Small. We show that if a \(q\)-skew derivation is not algebraic, then the GK dimension of the domain exceeds that of its invariants by at least one. In addition, if the domain has GK dimension less than 3 and the ground field is algebraically closed, then the invariants must be commutative.


GK dimension Invariants Automorphisms Derivations  Skew derivations 

Mathematics Subject Classification

16P90 16W25 


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Copyright information

© Springer-Verlag Wien 2015

Authors and Affiliations

  1. 1.Department of MathematicsDePaul UniversityChicagoUSA
  2. 2.Faculty of Computer ScienceBiałystok University of TechnologyBiałystokPoland

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